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INTERNATIONAL JOURNAL OF ENERGY RESEARCH

Int. J. Energy Res. (2010)

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1790

Exergy calculation of lithium bromidewater solution

and its application in the exergetic evaluation

of absorption refrigeration systems LiBr-H2O

Reynaldo Palacios-Bereche1,2, R. Gonzales3 and S. A. Nebra2,,y

1Mechanical Engineering Faculty, University of Campinas, UNICAMP, Campinas, Brazil2Interdisciplinary Centre of Energy Planning, University of Campinas, UNICAMP, Campinas, Brazil3Petrobras Energa Peru, Amador Merino Reyna 285, San Isidro, Lima, Peru

SUMMARY

The aim of this study is to present a methodology to calculate the exergy of lithium bromidewater solution(LiBr/H2O) widely used in absorption refrigeration systems, absorption heat pumps and absorption heat

transformers. As the LiBr/H2O solution is not ideal, it is necessary to take into account the activity of theconstituents in the chemical exergy calculation. Adopting the reference environment proposed by Szargut et al.,the chemical exergy of pure LiBr was obtained as well as the chemical and physical exergy of the LiBr/H 2Osolution. Results are reported in the temperature range between 5 and 1801C. In the literature, exergy values forLiBr/H2O solution are widely varied. This fact is due to different reference systems adopted to calculate exergy.Some cases in the literature are compared with that obtained with the methodology proposed in this study andwith the approaches of Koehler, Ibele, Soltes and Winter and Oliveira and Le Goff. Copyright r 2010 JohnWiley & Sons, Ltd.

KEY WORDS

absorption system; exergy; lithium bromide; chemical exergy; reference system

Correspondence

*S. A. Nebra, NIPE/UNICAMP, Cidade Universitaria Zeferino Vaz, P.O. Box 1170, Campinas, SP, 13084-971, Brazil.yE-mail: [email protected]

Received 23 April 2010; Revised 3 September 2010; Accepted 7 September 2010

1. INTRODUCTION

The bromide lithiumwater (LiBr/H2O) solution is

widely used as working fluid in absorption refrigera-

tion systems because of its nonvolatile and non-toxic,

besides being environmentally friendly by not con-

tributing to ozone depletion. Employing this solution

avoids the use of CFC refrigerants and its consequentenvironmental damage.

Low cost and easy handling are the advantages

of using water as refrigerant (despite its high

freezing point). On the other hand, low crystallization

temperature, high absorption capacity and low

viscosity are the advantages of LiBr/H2O solution as

absorbent [1].

Absorption refrigeration systems are attractive and

of increasing interest because they can be driven by

low-temperature heat sources and provide an excellent

way for converting solar energy or waste heat into

useful refrigeration [2,3]. They differ from compression

systems due to the use of a heat source as energy input

to operate; on the other hand, the refrigeration devices

based on compression systems need mechanical energy

to operate. This is the main advantage of absorption

systems; which can run on burning fuel or using waste

heat, recovered from other thermal systems.In exergy studies, it is necessary to calculate the

exergy of the working fluid at different points of the

system. In some studies found in the literature [36],

the exergy of the solution is calculated considering the

thermal component only (physical exergy), without

considering the chemical exergy.

In the literature there are some studies about

exergetic evaluation of absorption systems consider-

ing explicitly the chemical exergy for the pair

H2O/NH3 [7,8], but not many studies on absorption

Copyrightr 2010 John Wiley & Sons, Ltd.


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system considering the chemical exergy for LiBr/H2O

solution.

In terms of exergy destruction calculation (irrever-

sibilities), the balance of physical exergies gives correct

results due to the Gouy Stodola equation being

implicitly applied [3].

Moreover, the choice of reference species to obtain

chemical exergy does not influence the values ofinternal exergy losses but influences distinctly the

values of external losses, and hence also the calculated

values of the degree of thermodynamic perfection or

the exergetic efficiency [9].

On the other hand, in the analysis of components

such as absorbers or desorbers (generators), where

there are processes of separation and mixture, the

consideration of the chemical exergy of LiBr/H2O

solution would give differences in the results of

exergetic ratio of inlet and outlet type due to its

dependence on the numeric values of the exergy.

Moreover, values of exergy of the LiBr/H2O solu-

tion reported in the literature are widely varied; for thisreason there is the need to standardize the procedure

for exergy calculation of the LiBr/H2O solution

adopting a unique and general environment reference

system.

Thus, this study presents a methodological proposal

for the exergy calculation of a LiBr/H2O solution

adopting the reference environment proposed by

Szargut et al. [10] considering their physical and che-

mical components. This methodology represents a

useful tool for exergy analysis of mixture and separa-

tion process in absorption systems LiBr/H2O owing to

permit expanding the control volume including other

thermal systems such as direct-fired or cogeneration

systems; hence, an integrated analysis based in aunique reference system can be performed.

2. PROPERTIES OF THE LITHIUMBROMIDEWATER SOLUTION

For exergy calculation of the LiBr/H2O solution, the

thermodynamic properties are essential. The specific

enthalpy and entropy are indispensable to calculate

physical exergy, while the consideration of the

components activities is necessary to calculate the

exergy of the mixture [10,11].Some studies in the past intended to describe

the properties of the lithium bromide solution. The

most known study is probably the research by

McNeely [12].

Chua et al. [13] published an interesting study

correlating entropy and enthalpy of LiBr/H2O solu-

tions. In that paper, tables with values for enthalpy

and entropy were presented for a range of tempera-

tures and concentrations (01CoTo1901C and

0%oxo75%).

In a recent study, Kim and Infante Ferreira [14]

presented correlations for the calculation of enthalpy,

entropy, osmotic coefficient and Gibbs free energy

of the LiBr/H2O solution (01CoTo2101C and

0%oxo70%).

2.1. Solubility of pure LiBr in waterFigure 1 shows the solubility of pure LiBr in water as a

function of the temperature. The values are from

Boryta [15].

2.2. Enthalpy

The enthalpy of LiBr/H2O solution was evaluated

following the procedure described by Kim and Infante

Ferreira [14],

h yLiBr h1LiBrT;p11yLiBr

hlH2 OT;p1hET;p;m 1

where h1LiBrT;p is the molar enthalpy of the ideal LiBr

fluid, hlH2 OT;p is the molar enthalpy of pure water andhET;p;m is the enthalpy excess. These terms can be

calculated by Equations (2)(4). Values of the con-

stants employed are presented in Table I.

h1LiBr h1LiBr;01

Z TT0

C1pLiBrdT

V1LiBrT @V1LiBr

@T

pp0 2

h lH2 O h lH2 O;01

Z TT0

ClpH2 OdT

Z p

p0

VlH2OT @Vl

H2O

@T

!p

24 35 dp 3

h E yLiBr v R T2X6j1

2

i

@ai@T

1 i

2:v

@bi@T

p

mi=2 4

Figure 1. Solubility of pure LiBr in water.

Exergy calculation of LiBr-H2O solutionR. Palacios-Bereche et al.

Int. J. Energy Res. (2010) r 2010 John Wiley & Sons, Ltd.

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wherev is the dissociation number for the solute (v52).

C1p LiBr R T2

X2

j0

cj

Tj 5

V1LiBr R T b0 6

Clp H2 O R

X2j0

dj Tj 7

VlH2 O R

X2j0

ej Tj 8

aiX2j0

aij Tj 9

biX

2

j0

bij Tj 10

As considered by different authors [12,13], the

reference values herein used for enthalpy are: null va-

lues at 01C for pure water and for the solution at

50 wt%. Enthalpy in mass basis is calculated using

Equation (11). Results of the enthalpy, calculated with

the previous equations, are presented in Figure 2.

h h= Msol 11

Table I. Equation constants by Kim and Infante Ferreira [13].

j50 j5 1 j5 2

a1j 2.196316101

14.937232 103 6.5548406 105

a2j 3.810475 103

12.611535 106 3.6699691 108

a3j 11.228085 105 7.718792 107 11.039856 1010

a4j 1.471674106

19.195285 108 1.189450 1011

a5j 17.765821 106 4.937567109 16.317555 1011

a6j 1.511892 107

19.839974 109 1.27379 1012

b0j 4.417865 105

13.1149002 4.36112260

b1j 13.074104 1.86321 101 12.738714 101

b2j 4.080794 104

12.1608101 2.5175971 101

cj 9.440134105 5.842326108 0

dj 11.197193 101 1.83055 102 12.870938105

ej 12.66299 103 3.865189 106 17.464841 109

h1LiBr;0 57.1521 (kJ kmol1) hlH2 O;0 0

s1LiBr;0 147.5562 (kJ kmol1) slH2 O;0 0

T0 273.15 K p0 0.6108kPa

Figure 2. Enthalpy of lithium bromidewater solutions as a function of the concentration for different temperatures.

Exergy calculation of LiBr-H2O solution R. Palacios-Bereche et al.


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Where the Molar mass of the solution is calculated

based on the molar fraction and molar mass of the

components.

2.3. Entropy

For the entropy evaluation of the LiBr/H2O solution,

the correlation proposed by Kim and Infante Ferreira[14] is used:

s yLiBr s1LiBrT;p11yLiBr s

lH2 OT;p

yLiBr

n R ln m

m0

1

1sET;p;m 12

where the term s1LiBrT;p is the molar entropy of the

ideal LiBr fluid, and slH2 OT;p is the molar entropy of

pure water.

The third term is the entropy generation in

an ideal mixture (m0 is the standard molality:

m050,001 kmol kg1 of solvent) and the last term

sET;p;m is the additional entropy generation for a real

mixture process. These terms can be calculated byEquations (13), (14) and (15). Values of the constants

employed are shown in Table I.

s1LiBr s1LiBr;01

Z TT0

C1pLiBr

T dT

Z pp

0

@V1LiBr@T

p

dp 13

slH2O slH2 O;0

1

Z TT0

ClpH2 O

T dT

Z p

p

0

@VlH2 O

@T !

p

dp 14

s E yLiBr v R

X6j1

ai1i bi

2 vp1T

@ai@T

1 i

2:v

@bi@T

p

mi=2 15

Values of s1LiBr;0 and slH2 O;0

are shown in Table I. The

same reference values of enthalpy were used (01C for

pure water and solution at 50 wt%). The validity range

for Equation (12) is: mass fraction of LiBr,x,from 0 to

70% and solution temperatures, T, from 0 to 2101C.

Entropy in mass basis is calculated using Equation

(16). The results of entropy are presented in Figure 3.

s s= Msol 16

2.4. Activities

Water activity in the solution can be calculated by the

following expression [16]:

lnaH2 O fvm MH2O 17

2.4.1. Molality. Molality is normally defined as thenumber of moles of solute per kilogram of solvent. In

the calculation, following the procedure reported in

[14], the molality is redefined as kilomole of solute per

kilogram of solvent.

Then, the molality can be calculated from the LiBr

mole fraction (yLiBr) or the LiBr mass fraction (xLiBr)

as shown by the following equation:

m xLiBr

1xLiBr MLiBr

yLiBr

1yLiBr MH2O18

2.4.2. Osmotic coefficient. Kim and Infante Ferreira

[14] present the following expression to calculate the

osmotic coefficient of the LiBr/H2O solution. The

Figure 3. Entropy of lithium bromidewater solutions as a function of the concentration for different temperatures.



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termsaiand biare obtained by Equations (9) and (10):

f 11X6i1

ai:mi=21

p

2:n

X2i1

ibi:mi=2 19

2.4.3. Calculation of the LiBr activity in the solu-

tion. The LiBr activity in the solution can be

calculated from the water activity, applying the

GibbsDuhem equation, Equation (20), following the

method described in [17]. This method is utilized to

calculate the activity of a non-volatile component

when the activities of the other species are known:

Z 21

d ln aLiBr

Z 21

yH2 O

yLiBrdlnaH2O 20

The limits of integration are defined as follows [18]:

Point 1: General state, yLiBrPoint 2: Saturated state corresponding to the max-

imum solubility, yLiBr;sat

This upper limit of the integral was considered

because the solution at this state is in equilibrium with

pure lithium bromide, then the reference value for LiBr

activity at this point (point 2) corresponds to the pure

LiBr (aLiBr_251).

Substituting Equations (17), (18) and (19) into

Equation (20), after of operating and integrating,

Equation (21) is obtained. The results are presented in

Figure 4:

lnaLiBr v

"ln

yLiBr

1yLiBr MH2 O :1

X6i1

i12

i ai1i

pbi

2v

yLiBr

1yLiBr MH2 O

i=2#yLiBr;satyLiBr

21

whereb3 b4 b5 b6 0.

3. EXERGY CALCULATIONOF LIBR/H2O SOLUTION

Exergy of the lithium bromide solution can be

calculated as the sum of both physical and chemical

exergy:

ex exph1exch 22

3.1. Physical exergy

Physical exergy is the maximum work available when

the system is driven from its initial state (T,p) up to the

reference state (T0, p0) by means of a reversible

process, exchanging heat and work with the reference

environment only. If kinetic and potential components

of exergy are neglected, the physical exergy can be

calculated through the following expression:

exph hh0 T0 ss0 23

Figure 5 presents the physical exergy calculated by

Equation (23) for mass fractions of LiBr, x, ranging

from 0 to 70% and different T temperatures. The

reference state considered was T05 251C and p0 5

101.325 kPa. Enthalpies and entropies were calculated

according to the procedure described in the previous

section.

3.2. Chemical exergy

Chemical exergy is the maximum work that can be

achieved when a substance is driven from its equili-

brium state at the environment pressure and tempera-

ture (dead restricted state) to the equilibrium state ofequal chemical potentials (dead unrestricted state) by

means of processes that involve heat, work and mass

transfers with the environment. Because the LiBr/H2O

solution is not ideal, the following expression [11] is

used for chemical exergy calculation, as a function of

the activities and standard exergies of pure species:

ex ch 1= MsolXni1

yi ~e0i1

RT0Xni1

yi lnai

" # 24

Figure 4. Activities of water and LiBr in the solution, at 251C, as

a function of the mass fraction of LiBr.

Figure 5. Physical exergy of LiBr/H2O solution as a function of

the LiBr concentration.



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For LiBr/H2O solution:

exch 1= MsolyH2 O ~e0H2O

1yLiBr ~e0LiBr1

R

T0yH2 O lnaH2 O1yLiBr lnaLiBr 25

The chemical exergy equation above has two parts

as follows:

Standard chemical exergy of pure species:

exch;0 1= MsolyH2 O ~e0H2 O

1yLiBr ~e0LiBr 26

Exergy destruction due to dissolution process:

exch;dis~RT0Msol

yH2 O lnaH2 O1yLiBr lnaLiBr 27

Figure 6 shows schematically the methodology to

calculate the exergy components for LiBr/H2O solu-

tion. The path from initial solution at x, p and T to

reach the dead state according to Kotas can be

observed [11]. The values 2.5 105 and

8.7 104 mol kg1 H2O in Figure 6 are the conven-

tional standard molarities of the reference species dis-solved in sea water: Li1 and Br, respectively,

according to [10].

3.2.1. Standard chemical exergies. The standard che-

mical exergies for water, lithium and bromide were

found in [10]. Rivero and Garfias [19] accomplished a

revision and re-calculation of the standard chemical

exergies of elements but their results, for the substances

Li and Br, do not present significant differences

(deviations around 0.2%) in comparison with the

values reported in [10].

~e0H2 O 0:9 kJ=mol

~e0Li 393 kJ=mol

~e0Br2 101:2 kJ=mol

The standard chemical exergy for the LiBr compound

can be calculated following Kotass proposal [11]:

~e0 D ~g0f1Xni1

~e0el 28

In Equation (28), n indicates the number of ele-

ments, while subscript el indicates the element.

Li1 12

Br2 ! LiBr 29

~e0LiBr D ~g0LiBr1~e

0Li1

12~e0Br2 30

whereD ~g0LiBr 342:0 kJ mol

1 20

The result of Equation (28) is: ~e0LiBr 101:6 kJ=mol.This value will be used later in Equation (25) for che-

mical exergy calculation of the LiBr/H2O solution.

Figure 7 presents the chemical exergy calculated as a

function of standard chemical exergies of solution

components (exch;0) as indicated in Equation (26), the

variation of chemical exergy due to the dissolution

process (exdis), calculated according to Equation (27)

and the total chemical exergy at 251C calculated by the

sum of previous terms according to Equation (25).

Figure 8 presents the total exergy by summing up

both physical and chemical terms, calculated accordingto Equation (22).

Figure 6. Path from initial state at x, Tand p to the dead state

according to this studyExergy components of LiBr/H2O

solution.

Figure 7. Standard chemical exergy (exch;0), variation of

chemical exergy due to the dissolution process (exdis) and total

chemical exergy at 251C of LiBr/H2O solution as a function of

LiBr concentration (mass basis).

Figure 8. Total exergy, chemical and physical of LiBr/H2O

solution as a function of LiBr concentration (mass basis).



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4. STUDY OF CASESCOMPARISON WITH OTHERAPPROACHES

4.1. Approach of Koehler et al. [1]

Koehler et al. [1] present an approach for exergy

calculation of LiBr/H2O solution, which considers thatthe least potential of a solution for doing useful work is

given when it is in a saturated state at T0 and p0 (the

minimum free energy state defines the zero exergy level

at T and p defined). Thus for a given environmental

state, the exergy c can be treated as a state function

and it can be chosen as a convenient path from any

given state to the defined dead state. The path to the

reference state is shown in Figure 9.

cT;p; x cxT;p1c0x 31

The termcx(T,p) is the temperature- and pressure-

dependent part of the exergy (thermal term) while the

termc0(x) represents the exergy of dissolution. To find

c0(x), these authors imagine a mixture at T0 and p0undergoing a change of state from a given concentra-

tionx to the dead state xsatby admitting an amount of

solute at T0 and p0. Applying the first and second law

of thermodynamics to this process, the authors get

an equation for exergy calculation of the LiBr/H2O

solution.

Thus, the minimum level of exergy corresponds to

the saturated solution xsat while the highest value

corresponds to pure water. In order to maintain the

consistency in exergy balances, these authors should

calculate the exergy of pure water according to their

correlations, which consider the saturate state xsat of

LiBr/H2O solution as reference state.

4.2. Approach of Oliveira and Le Goff [21]

Oliveira and Le Goff [21] also present an approach for

exergy calculation of LiBr/H2O solutions. These

authors consider a reference state at T0 and p0 and

equilibrium compositions of the mixture at T0 and p0.

The reference conditions adopted for the LiBr/H2O

solution were T05 251C, p05 100 kPa, pure water

(x5 0) and a solution at x05 20 wt%. Hence, the

exergy of mixture can be calculated from the properties

of pure water and the reference solution at x0. The

path to the reference state is shown in Figure 10.

4.3. Comparison of results with otherapproaches and studies

Three cases of the literature are studied and compared.The first is an absorption heat pump and the second

and third are absorption refrigeration systems. Calcu-

lations were performed using equation engineering

solver (EES) [22].

The absorption heat pump evaluated in Koehlers

study [1] is presented in Figure 11. The model con-

sidered by these authors consists of an internal and an

external system. The external system represents the

connection between the internal system and the

surroundings. The internal system is a standard

absorption cycle containing: evaporator, condenser,

absorber, generator, pump, two expansion valves and

two heat exchangers.

Table II shows the operational conditions of thissystem. Specific exergies reported by Koehler et al. [1]

are compared with specific exergies calculated by

Oliveira and Le Goff [21] approach and calculated by

the procedure proposed in Section 3 of this study.

Enthalpies and entropies were calculated using the

procedure described in Section 2 according to Kim and

Infante Ferreira [14].

The reference temperature adopted by Koehler et al.

[1], in exergy calculation, was T05 51C. On the other

hand, the methodology proposed in this study as well

Figure 9. Path from initial state at x, Tand p to the reference

state according to the approach of Koehler et al. [1]Exergy

components of LiBr/H2O solution.

Figure 10. Path from initial state at xM,Tandpto the reference

state according approach of Oliveira and Le Goff [21].

Figure 11. Absorption heat pump evaluated by Koehleret al. [1].



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as Oliveira and Le Goff [21] approach adopt T05251C

as reference temperature.

In Table II, negative values for enthalpies of LiBr/

H2O solution (points 5, 6PU, 6, 7G, 7, 8) can be

observed, which indicate that the references for enthalpy

are different from that adopted by McNelly [12] and

Kim and Infante Ferreira [14]. For the next cases some

constants were adjusted in Koehlers exergy equation in

order to get exergy values according to the graphics

reported by these authors [1] using correlations of Kim

and Infante Ferreira [14] to calculate properties.

It can be observed that specific exergies for pure

water are negative in points: 1S and 1 for Oliveira andLe Goff approach [21] as well as this study approach

due to these points are below the reference state. On

the other hand, Koehler et al. [1] reported the highest

values of exergy for pure water and lower exergies

values of LiBr/H2O solution (negatives values in points

7 and 8). The approach of this study shows the highest

values for LiBr/H2O solution.

It was not possible to compare irreversibilities and

exergetic efficiencies reported by these authors, in this

case, because they neither inform mass flows nor the

pressure of the external points of the system (points

EWI, EWE, CWI, CWE, AWI, AWE, GWI, GWE).

In the second case, the absorption refrigeration

system of single effect evaluated by Sencan et al. [5] is

shown in Figure 12. This system is composed of a

condenser, generator, solution heat exchanger, absor-

ber, evaporator, pump, solution expansion valve and

refrigerant expansion valve.

Table III shows operation conditions for the system

as well as specific exergies reported by the authors [5]

and calculated by approaches described in the previous

sections. For all approaches the reference temperature

was adopted as T05 251C.

Sencan et al. [5] also indicate 251C as reference tem-

perature but they do not indicate the reference pressure

nor the chemical composition of reference state. The

internal system pressures were calculated considering the

temperature at condenser outlet and evaporator outlet.

Thus, the lower and the higher pressures obtained for

the system were 1.002 and 7.381 kPa, respectively. It was

not possible to compare the results of irreversibilities or

exergetic efficiencies reported by the authors [5] as

they did not report values of pressure for points of the

external circuit (11, 12, 13, 14, 15, 16, 17, 18).

From Table III it can be observed that specific

exergies of LiBr/H2O solution in Sencanet al. [5] study

are lower in comparison with the values obtained from

approaches of this study and Oliveira and Le Goff [21].

In comparison with Koehler et al. [1] approach, spe-

cific exergies of LiBr/H2O solution of Sencan et al. [5]

are lower than Koehler et al. values [1] for x 557.59%

but they are higher for x 558.15%.

Figure 12. Absorption refrigera tion system evaluated by Sencan

et al. [5].

Table II. Operational conditions for absorption heat pump evaluated by Koehler et al. [1]Comparison of specific exergy values with

other approaches.

Koehleret al. [1]

Oliveira and

Le Goff [21] This study

M(kg/s) T(K) P (kPa) vfrac x% h (kJkg1) s(kJkg1 K1) c (kJkg1) ex1y (kJkg1) ex2y (kJkg1)

1S 1 280.2 1 1 0 2513.76 8.9610 647.72 157.6 107.7

1 1 304.2 1 1 0 2558.96 9.1332 645.03 158.6 108.6

2 1 357 15.73 1 0 2656.09 8.1181 1024.51 229.4 279.4

3S 1 328.2 15.73 0 0 230.46 0.7686 643.15 5.834 55.79

3 1 317.4 15.73 0 0 185.26 0.6276 637.18 2.4 52.36

4 1 280.2 1 0.063 0 185.26 0.6597 628.22 8.529 41.43

5 4.713 303.2 1 0 51.1 174.05 0.2831 53.74 87.48 447.7

6PU 4.713 303.2 15.73 0 51.1 174.04 0.2831 53.76 87.49 447.7

6 4.713 330.9 15.73 0 51.1 113.92 0.4721 61.30 91 451.2

7G 3.713 388.2 15.73 0 64.9 20.02 0.6848 9.87 214.5 658.6

7 3.713 345.7 15.73 0 64.9 96.36 0.4680 6.14 200.2 644.3

8 3.713 331.1 1 0.009 64.9 96.33 0.4672 5.92 199.8 643.8

Values of enthalpies, entropies and specific exergies reported by Koehler et al. [1].yEnthalpies and entropies were calculated by equations of Kim and Infante Ferreira [14] according to item 2 of this study.



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Regarding the exergy of pure water, Sencanet al. [5]

report negative values at outlet of condenser, expan-

sion valve of refrigerant and evaporator (points 8, 9

and 10).

In a recent study Arora and Kaushik [3] evaluated

an absorption refrigeration system of single and double

effect. The configuration of the absorption refrigera-

tion system of single effect studied by these authors isthe same as the configuration shown in Figure 12.

Table IV shows the operational conditions for this

system. Specific exergies in each point of the cycle were

calculated by the approaches described in previous

sections. Arora and Kaushik [3] do not report values of

exergy in each point of the cycle.

Unlike the previous cases, Arora and Kaushik [3]

evaluate irreversibilities in each system component

considering only the internal circuit, calculating the

exergy of the heat flows.

In this study irreversibilities generated in each sys-

tem component are calculated by means of exergy

balance.

IX

_min exinX

_mout exout _Q

1T0

Tr

_Wvc 32

In Equation (32)Tris the temperature at the control

surface where the heat transfer is taking place. Aroraand Kaushik [3] define the temperature Tr for each

component; thus, for the generator Tr5Tg5 87.81C,

for the evaporator Te5 7.21C and for the condenser

and the absorber Tr5Tc5Ta5 37.81C.

To calculate exergetic efficiencies, the rational effi-

ciency concept [11] is used:

Zex roduct

Fuel 33

This definition is applied to components where it is

possible to define aproduct. This definition follows that

recommended by Szargut et al. [10] and Kotas [11].

The latter one being named rational efficiency. On the

Table III. Operational conditions for absorption heat pump evaluated by Sencanet al. [5]Comparison of specific exergy values with

other approaches.

Secan et al. [5] Koehler et al. [1] O live ira a nd Le Goff [21 ] Th is stud y

m (kgs1) T(1C) x(%) c (kJkg1) cy (kJkg1) ex1y (kJkg1) ex2y (kJkg1)

1 0.5 40 57.59 12.95 20.87 130.8 530.4

2 0.5 40 57.59 12.95 20.87 130.8 530.4

3 0.5 67.6 57.59 22.09 25.67 135.6 535.2

4 0.495 80 58.15 29.73 26.29 143.3 546.3

5 0.495 52 58.15 21.52 19.59 136.6 539.6

6 0.495 52 58.15 21.52 19.59 136.6 539.6

7 0.005 80 0 99.07 745.7 124.6 174.5

8 0.005 40 0 3.12 622.6 1.432 51.399 0.005 7 0 3.12 614.5 6.601 43.36

10 0.005 7 0 161.7 463.8 157.3 107.4

Values reported by the authors.yValues calculated in this studyProperties calculated according Kim and Infante Ferreira [14] procedure.

Table IV. Operational conditions for absorption refrigeration system evaluated by Arora and Kaushik [3]Comparison of specific

exergy values for different approaches.

Koehleret al. [1]

Oliveira and


m (kg s1) T(1C) p (k Pa) Vfra c x(%) h (kJkg1) s(kJkg1 K1) c (kJkg1) ex1 (kJ kg1) ex2 (kJkg1)

1 9.035 37.8 1.016 0 55.42 91.539 0.2288 32.56 114.9 501.4

2 9.035 37.8 6.558 0 55.42 91.543 0.2288 32.57 114.9 501.4

3 9.035 66.2 6.558 0 55.42 148.953 0.4054 37.35 119.7 506.2

4 8.035 87.8 6.558 0 62.32 221.19 0.4787 10.42 180.4 608.7

5 8.035 53.08 6.558 0 62.32 156.635 0.2905 1.882 171.8 600.2

6 8.035 53.08 1.016 0.002251 62.32 156.635 0.2906 1.881 171.8 600.2

7 1 87.8 6.558 0 0 2664.211 8.58 731.9 110.8 160.7

8 1 37.8 6.558 0 0 158.301 0.5428 622.2 1.021 50.98

9 1 7.2 1.016 0.05155 0 158.301 0.5661 615.2 5.911 44.05

10 1 7.2 1.016 0 0 2513.751 8.968 465.7 155.4 105.5



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other hand, for dissipative components, we used the

ratioz as exergetic effectiveness of inlets and outlets.

The inlet exergy, in this ratio, corresponds to the

exergy of all the exergy carriers that get into

the control volume considered. On the other hand, the

outlet corresponds to the exergy of all the exergy

carriers that go out the control volume.

The ratio z is defined in Equation (34).

zex

P _mout exout1 _Wout1 _Qout ZcarnotP

_min exin1 _Win1 _Qin Zcarnot34

For instance, in the absorber, it is defined as:

zex;a _m1 ex11 _Qa 1T0=Ta

_m10 ex101 _m6 ex635

Table V shows irreversibilities calculated by Arora

and Kaushik [3] and by exergy balances according to

the methodology proposed in Section 3 and according

to the approaches of Koehler et al. [1] and Oliveira and

Le Goff [21]. Furthermore, irreversibilities are calcu-

lated by Gouy Stodola equation (Equaiton (36)) using

the correlations reported in item 2 of this study.

Table VI shows the ratio, z, calculated by each

approach.

From Table V it can be observed small differences

between irreversibilities reported by [3] and re-

evaluated using the procedure of Kim and Infante

Ferreira [14] for property calculations. The highest

difference is in absorber (5.68%). Regarding irreversi-

bilities calculated considering the different approaches,

it can be observed that differences are not significant;

owing to the fact that exergy balances the references

values cancel. Moreover, the irreversibility calculation

can be performed without calculating exergies, con-

sidering the Gouy Stodola equation:

I T0XOUT

_mout SoutX

IN

_min: s inX

r

_Qr

Tr

" # 36

Rational exergetic efficiency (Zex) resulted in thesame value for all the approaches. It was calculated in

generator, evaporator and heat exchanger of solution

resulting in 89.3, 42.3 and 63%, respectively.

The ratio of inlet and outlet (x) resulted high in all

the cases. There were little differences due to the

different values of the different approaches. In

Table VI it can be observed that this study presents the

highest values ofx in system components where LiBr/

H2O solution is involved. This a consequence of the

high value of the standard chemical exergy considered.

Exergetic efficiencies calculated by the approach of

Oliveira and Le Goff [21] present intermediate values

between this study and the Koehler approach [1].

Thus, it can be observed that, in the literature, the

values of exergy for LiBr/H2O solution are widely

varied because the reference conditions and chemical

composition of the reference environment are unlike in

the different approaches. There are also some differ-

ences in property values such as enthalpy or entropy of

the LiBr/H2O solution.

For instance, Sencan et al . [5] report ex5-

c5 19.95kJkg1 for x557.59% and T5401C; and

ex5c5 21.52 kJkg1 forx5 58.15% andT5 521C. In

[4], Talbi and Agnew report ex5c5227.817 kJkg1

Table V. Irreversibilities in kW for each component of the systemComparison of results in system evaluated by Arora

and Kaushik [3].

Gouy Stodola

equation

Arora and

Kaushik [3]

Koehler

et al. [1]

Oliveira and


(1) (2) (3)

Absorber 66.24 70.48 67.24 66 66.28 66.47

Condenser 6.60 6.61 6.60 6.60 6.60 6.60

Evaporator 86.25 86.28 86.25 86.25 86.25 86.25

Generator 57.15 55.57 57.15 57.39 57.12 56.93

Heat exchanger of solution 27.69 25.08 25.36 25.36 25.36 25.36

(1) Values calculated in this studyEntropy calculated according Kim and Infante Ferreira [14] procedure. (2) Values reported byArora and Kaushik [3]Properties calculated according to Pa tek and Klomfar [23] (3) Values calculated in this studyPropertiescalculated to according Kim and Infante Ferreira [14] procedure.

Table VI. Exergetic ratio of inlets and outlets xComparison with approaches of Koehler et al. [1] and Oliveira and Le Goff [21].

Koehleret al. [1] Oliveira and Le Goff [21] This study

Absorber 86.27 94.59 98.59

Condenser 99.10 94.04 95.89

Evaporator 85.98

Generator 93.43 96.47 98.89

Heat exchanger of solution 93.29 98.98 99.73



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for x559.5% and T5471C; although there are slight

differences in temperatures and concentrations the value

reported by Talbi and Agnew [4] is quite big in com-

parison with that reported by Sencan et al. [5].

Misra et al. [6] consider the physical exergy and the

chemical exergy of the pure water contained in the so-

lution. They report ex533.91kJkg1 for x556.43%

and T5341C which is almost two times the valuereported by Sencan et al. [5] under similar conditions.

Consequently, there is the need to standardize the

procedure for exergy calculation of LiBr/H2O solution

and this study intends to contribute to this objective

proposing a methodology of exergy calculation con-

sidering the reference environment of Szargut et al. [10].

Furthermore, this proposal permits an integrated

analysis considering the external losses of exergy or

considering a control volume that includes more pieces

of equipment as the direct-fired system. For instance,

Figure 13 shows an absorption refrigeration system of

single effect together with a cooling tower. The heat

duty in the condenser and absorber is removed by thewater flow of the cooling tower. The local temperature

considered is 291C but for exergetic analysis standard

conditions are considered: T05251C and

p05 101.325 kPa. The temperature T7 is calculated

considering the boiling temperature of the solution at

concentration x3, on the other hand, the temperature

T4 is the equilibrium temperature at concentration x4according to Herold and Radermacher [24].

Furthermore, the exergetic evaluation of a direct

fired system can be accomplished. In this case streams

of natural gas, air and exhaust gases should be con-

sidered according to Figure 14 (25, 26 and 27). In order

to take into account heat losses to the environment,

an efficiency of heat transfer Zht;g in the generator isadopted as 0.84 [25]:

_Qg Zht;g _vgas LHVgas 37

The temperature of exhaust gases is calculated by a

balance of enthalpies using JANAF tables of EES,

considering heat losses to environment of 5%. Thus,

the temperature of exhaust gases resulted as 202.51C.

Table VII shows the results of the exergy calculation

with the proposed methodology in each point of this

system. Table VIII shows the heat exchanged, irre-

versibilities and exergetic efficiencies. It can be

observed the low value of the exergetic efficiency for

the direct-fired system (2.5%), which indicates that theabsorption refrigeration systems are more appropriate

to operate together with cogeneration systems or

utilizing of some waste heat. The values ofzexare very

high owing to the high numerical values of input and

output exergy and the consideration of adiabatic

devices. In the case of a hot-water-driven system, the

element with higher irreversibility is the cooling tower,

due to the high loss of mass that occurs in this element.

The irreversibility of cooling tower represents 20.97%

of the total irreversibility of the system.

Still in this analysis there are some values of negative

exergy for water streams because the pressure of these

streams is below the reference pressure p0. This effectcan be observed in rows 9 and 10 of Table VII.

In relation to the reference states chosen by other

authors for exergy calculation of LiBr-H2O solution,

there are some issues that deserve mention. Koehler

et al. [1] approach considers the minimum exergy level

for the maximum solubility state of the solution while

the highest values of exergy correspond to pure water.

Hence, the minimum exergy level corresponds to the

minimum of free energy at the reference temperature

and pressure adopted. These authors preferred to

adopt the local environmental conditions as reference

state. In order to obtain consistent results, the exergy

of pure water should be calculated with an appropriate

equation reported by [1]; this equation takes into ac-count the properties of the solution at saturated state,

of pure water and pure LiBr, at the reference

temperature. Exergy negatives values can be obtained

depending on the solution temperature and con-

centration compared with the reference conditions.

This effect can be observed in Table II, points 7 and 8.

Different from Koehler, the Oliveira and Le Goff [21]

approach adopts as reference conditions fixed values of

temperature and pressure: T05251C, p05100kPa, and

also pure water and a solution concentration of 20%.

Adopting variable reference conditions of tempera-

ture and pressure to calculate exergy has positive and

Figure 13. Absorption refrigeration system of single effect with

cooling tower.

Figure 14. Generator of the direct-fired absorption refrigeration

system.



DOI: 10.1002/er


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negative aspects. In some cases, to analyze an isolated

refrigeration system adopting the local temperature

and pressure can be useful. But this selection will be

difficult for any comparison between system perfor-

mances working in different conditions.

5. CONCLUSIONS

In this paper, a methodology for the exergy calculation

of the lithium bromidewater solution, used in

absorption refrigeration systems, was presented. The

Table VII. Operational conditions at each point of the single-effect system.

Pto. m (kgs1) P(kPa) T(1C) X(%LiBr) h (kJkg1) S(kJkg1 K1) exph (kJkg1) exch (kJkg1) ex to (k J kg1)

1 1.177 0.84 32.9 54.9 80.6 0.205 0.117 494.2 494.3

2 1.177 7.5 32.9 54.9 80.7 0.205 0.123 494.2 494.3

3 1.177 7.5 62.1 54.9 140.4 0.391 4.3 494.2 498.4

4 1.042 7.5 89 62 221.1 0.489 11.2 593.2 604.4

5 1.042 7.5 53.1 62 153.7 0.293 2.2 593.2 595.4

6 1.042 0.8 47.3 62 153.7 0.300 0.1 593.2 593.3

7 0.135 7.50 73.5 0 2637 8.441 124.9 49.96 174.9

8 0.135 7.50 40.3 0 168.8 0.576 1.5 49.96 51.45

9 0.135 0.84 4.5 0 168.8 0.608 8.1 49.96 41.86

10 0.135 0.84 4.5 0 2508.7 9.038 181.3 49.96 131.3

11 16.55 424.7 95 398.2 1.250 30.2 49.96 80.13

12 16.55 145.2 89 372.8 1.181 25.3 49.96 75.22

13 20.46 424.7 29 121.9 0.423 0.4 49.96 50.39

14 20.46 274.05 33.8 141.6 0.488 0.7 49.96 50.66

15 20.46 274.05 33.8 141.6 0.488 0.7 49.96 50.66

16 20.46 145.2 37.7 157.9 0.541 1.1 49.96 51.1

17 13.58 424.7 12 50.8 0.180 1.5 49.96 51.5

18 13.58 145.2 6.5 27.5 0.099 2.5 49.96 52.51

19 14.37 101.3 29 74.4 5.870 0.1 0 0.0922420 14.64 101.3 35 128.9 6.050 1.9 0 1.897

21 0.266 101.325 29 121.6 0.423 0.1 49.96 50.07

22 20.46 101.325 37.7 157.9 0.541 1.1 49.96 51.09

23 20.46 101.325 29 121.6 0.423 0.1 49.96 50.07

24 20.46 424.7 29 121.9 0.423 0.4 49.96 50.39

25 0.0097 101.325 29 8.3 10.840 0.057 51254 51254

26 0.1894 101.325 29 74.4 5.870 0.092 0 0.09224

27 0.1983 101.325 202.5 197.5 7.701 42.76 65.4 108.2

Table VIII. Heat transfer, irreversibilities, exergetic efficiency (Zex) and exergetic ratio (zex) for the absorption refrigeration system of

single effect shown in Figure 13.

Component Q (kW) I (kW) Zex (%) zex (%)

Heat exchanger solution 70.29 4.46 52.35 99.63

Condenser 333.25 7.67 99.28

Evaporator 315.93 9.764 58.24 98.62

Absorber 403.92 13.3 99.18

Refrigerant expansion valve 1.29 81.37

Solution expansion valve 2.242 99.64

Cooling water pump 3.126 60.44 99.70

Solution pump 0.0053 47.45 99.99

Cooling tower 737.17 14.95 96.08

Generator: hot-water-driven system 421.23 14.45 82.22 99.25

Generator: direct fired system 421.23 410.7 13.38 60.2

Global system: hot water driven system 71.26 14.29 97.28Global system: direct fired system 467.50 2.65 60.99



DOI: 10.1002/er


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methodology encompasses the calculation of the

currently called physical and chemical exergy, taking

into account the dissolution exergy [10,11].

The thermodynamic properties of the solution,

enthalpy and entropy, were obtained from the biblio-

graphy. Owing to the fact that the LiBr/H2O solution

is not ideal, to calculate chemical exergy the concept of

activity must be applied. Water activity was obtainedthrough the osmotic coefficient, while for LiBr activity

in the solution, a correlation was developed from water

activity by using the GibbsDuhem equation. The

results show that LiBr activity in the solution is almost

null for low concentrations, but increases abruptly

close to the solubility limit.

In relation to chemical exergy, the term calculated

with standard chemical exergies is the highest and

presents a great increase with LiBr concentration. The

term of chemical exergy related to the dissolution

process was negative due to the exergy destruction,

inherent to this process, following the trend of the

Gibbs free energy reduction for the solution. Thisindicates that the work input is necessary to separate

the dissolution components.

Regarding total exergy, which is the sum of physical and

chemical exergies, it increases with LiBr concentration.

The lack of a pre-established methodology has led

several authors to perform exergy calculations report-

ing widely varied exergy values for the LiBr/H2O

solution. Some of these studies are limited to the cal-

culation of irreversibilities and exergetic efficiency of

the overall system considering only pure water prop-

erties. Thus, there is the need to adopt a unique

methodology for exergy calculation of LiBr/H2O so-

lution. Koehleret al. [1] and Oliveira and Le Goff [21]

deal with this topic proposing different reference sys-tems. This study proposes the adoption of a universal

reference system, which permits extending the control

volume to more complex systems, including the hot

source, doing a unique integrated analysis based in a

unique reference system for exergy calculations.

Thus, it is possible to compare on the same basis a

direct-fired absorption system, burning some fuel, or a

cogeneration system that could operate jointly with the

absorption system.

APPENDIX A: NUMERICAL

EXAMPLE OF EXERGYCALCULATION FOR A SPECIFICPOINT

It considered the general point: T5 37.81C, p5

1.016kPa, xLiBr5 55.42%

MLiBr86:85 kg kmol1

MH2 O18:02 kg kmol1

x1w xLiBr=100 0:5542

Molar fraction

yH2O 1x1w MLiBr=1x1w

MLiBr1x1w MH2O 0:795

yLiBr 1yH2 O 0:205

Molar mass of solution

Msol yH2 O MH2 O1yLiBr MLiBr32:13 kg kmol1

Molality

m x1w=1x1w MLiBr 0:01431

A.1. Enthalpy calculation

T05 273.15 K,R 5 8.314 kJ kmol1 K1

h1LiBr h1LiBr;0

R c0 1

T

1

T0

1

c1

2

1

T2

1

T20

1c2

3

1

T3

1

T30 1R b0112b02

T pp0

10 983 kJ kmol1

h lH2 O h lH2O;01R

d0 T T01d1

2 T2 T20 1

d2

3T3 T30

1R

e0 2 e2 T1e2 T2 p p0

2853 kJ kmol1

h E yLiBr v R T2X6j1

2

i

@ai@T

1 i

2:v

@bi@T

p

mi=2

2950 kJ kmol1

h yLiBr h1LiBrT;p11 yLiBr

h lH2OT;p1h ET;p;m

2966 kJ kmol1

h h= Msol 92:31kJkg1

A.2. Entropy calculation

s1LiBr s1LiBr;0 R

c0

2

1

T2

1

T20

1

c1

3

1

T3

1

T20

1

c2

4

1

T4

1

T40

R b00

b02

T2

pp0

9:952kJkmol1 K1

slH2 O slH2 O;0

1R

d0 ln T

T0

1d1 TT01

d2

2 T2 T20

R

e112e2 T pp0

9:783kJkmol1 K1



DOI: 10.1002/er


14/16

sE yLiBr v R X6j1

ai1ibi

2 vp1T

@ai@T

1 i

2 v

@bi@T

p

mi=2

3:35kJkmol1 K1

s yLiBr s1LiBrT;p11yLiBr s

lH2 OT;p

yLiBr n R

ln m

m0

1

1sET;p;m7:503kJkmol

1 K1

s s= Msol 0:2335kJKg1 K1

A.3. Physical exergy

Enthalpy and entropy of reference for LiBr-H2O

solution considered: T0;r

25C, p0;r

101:325 kPa

and xLiBr5 55.42%

h0;r 66:83kJkg1

s0;r 0:1495kJkg1 K1

exph hh0;r T0;refss0;r

92:3166:83251273:150:23350:1495

0:44kJkg1

A.4. Chemical exergy calculation

Osmotic coefficient

f 11X6i1

ai mi=21 p2n

X2i1

ibi mi=2 3:762

Activity H2O

lnaH2 O fvm MH2 O

3:76220:0143118:02

1:9402

aH2O 0:1437

Molality in saturated state xLiBr,sat5 62.23%

msat xLiBr;sat

1xLiBr;sat MLiBr0:01897 kmol kg1

Activity LiBr

Substitutingm in Equation (21)

ln aLiBr v

"ln m1

X6i1

i12

i

ai1ipbi

2v

! mi=2

#msatm

3:204

aLiBr 0:04062

Standard chemical exergy of pure species

exch;0 1= MsolyH2O ~e0H2 O

1yLiBr ~e0LiBr

1=32:13 0:79590010:205101 600

670:6 kJ kg1

Exergy destruction due to dissolution process

exch;dis~RT0Msol

yH2 O lnaH2O1yLiBr lnaLiBr

8:314298:15=32:13 0:795 1:940210:205 3:204

169:67 kJ kg1

Chemical exergy

exch 670:61 169:67 500:9 kJ kg1

Total exergy

exto 0:441500:9 501:3 kJ kg1

NOMENCLATURE

a 5 activity

Cp 5 specific heat at constant pressure

(kJ kg1 K1)Cp 5molar specific heat at constant pressure

(kJ kmol1 K1)

ex 5 specific exergy (kJ kg1)

h 5 enthalpy (kJ kg1)h 5molar enthalpy (kJ kmol1)

I 5 irreversibility (kW)

LHV 5 lowing heating value (kJ m3)

m 5molality (mol kg1 of solvent)

m 5molecular mass (kg kmol1)

p 5pressure (kPa)_Q 5heat flow rate (kW)R 5universal gas constant

(kJ kmol1 K1)

s 5 entropy (kJ kg1 K1)

s 5molar entropy (kJ kmol1 K1)

T 5 temperature (K)

v 5dissociation number (5 2 for LiBr)

_vgas 5 volumetric flow of natural gas_W 5power (kW)V 5molar specific volume (m3 kmol1)

vfrac 5 vapour fraction

x 5 concentration of solute in massy 5mole fraction

Greek letters

~e0 5 standard chemical exergy

(kJ kmol1)

D 5difference

Z 5 efficiency

n 5dissociation number for the solute

r 5density



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f 5osmotic coefficient

D ~g0f 5 standard molar Gibbs free energy of

formation (kJ kmol1)

c 5 specific exergy calculated by Koehler

et al. [1] and Sencan et al. [5]

x 5 exergetic ratio of inlet and outlet

Subscripts

0 5 reference state

1,2y 5points of the cycle

a 5 absorber

Br2 5molecular bromide

c 5 condenser

ch 5 chemical

dis 5dissolution

e 5 evaporator

ex 5 exergetic

g 5 generator

gas 5natural gas

H2O 5water

ht,g 5heat transfer in the generatorin 5 inlet

Li 5 lithium

LiBr 5 lithium bromide

M 5mixture

out 5outlet

ph 5physical

sat 5 saturation

sol 5 solution

to 5 total

vc 5 control volume

Superscripts

* 5 saturate state of pure solventN 5 ideal fluid for solute species

E 5 excess property

l 5 liquid phase

ACKNOWLEDGEMENTS

The authors wish to thank CNPq (PQ 10-307068/2006-4) and FINEP (Contract FINEPFUNCAMP Nr.01/06/004700).

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DOI: 10.1002/er

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